Adaptive Implicit Inverse Control for a Class of Discrete-Time Hysteretic Nonlinear Systems and Its Application

This article proposes an adaptive implicit inverse control scheme for a class of discrete-time hysteretic nonlinear systems. The Prandtl-Ishlinskii model is employed to characterize the hysteresis loop in piezoelectric actuator. The main contributions are as follows: 1) by using the dynamic surface control technique, which introduces the digital first-order low-pass filter, the original control system are not required to be transformed into an unknown special form; 2) the hysteresis implicit inverse compensator is constructed to overcome the hysteresis, which implies that the hysteresis item coupled with control signal is treated as the temporary control signal from which the method of searching the approximately control signal is designed; and 3) by employing the experimental platform of the piezoelectric positioning stage, the experimental verifications of the designed discrete-time adaptive controller are implemented. It is proved that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and the experimental results show the effectiveness of the proposed adaptive dynamic surface discrete-time motion control (ADSDMC) scheme.